The use of high speed rotating machinery is very important in modern industry; often, maximum operating speed is limited by the onset of serious vibrations caused by an imbalance of the rotoring portion of a machine. If the machine is operating at a rotational speed well below the first flexural critical speed of the rotor shaft, the shaft can be considered to be stiff, in which case the imbalance can be described as a displacement and/or misalignment of the principal axis of inertia of the rotating mass relative to the axis of rotation. This imbalance is the result of unequal mass distribution about the axis of rotation. At higher rotation speeds, shaft deformation becomes a factor, and the shaft must be considered as being flexible. The balancing procedure in the flexible-shaft situation is termed flexible-rotor balancing or "modal balancing". Balancing of either rigid or flexible rotors is accomplished by the placement of compensating balance masses along or about the rotor. The size and placement of these balance masses is usually determined by testing the rotor using a balancing machine, as described in chapter 39 of "Shock & Vibration Handbook, Third Edition" (1988), edited by Cyril M. Harris, published by McGraw-Hill Book Company, New York. Manual balancing is effective in dealing with rigid rotor vibrations, but is relatively ineffective in dealing with flexible rotor vibrations, because a destabilizing positive feedback process becomes dominant in determining rotor dynamics when the rotor operates at speeds which cause significant shaft flexure; a very small initial imbalance becomes magnified in the flexible-rotor case because the shaft deforms in response to the net centrifugal force, and the deformation causes additional imbalance. This positive feedback process cannot be influenced by manual balancing, because manual balancing affects only the initial mass distribution and cannot respond to shaft flexure. On the other hand, automatic balancing, which is a control process, provides negative feedback which can compensate for the destabilizing effects of the positive feedback attributable to shaft flexure. With automatic balancing, the rotor can be operated at significantly higher speeds, and with less bearing wear, than without automatic balancing.
However, prior art automatic balance systems are costly and complex. A prior art automatic balancing system might require electronic sensors to detect the imbalance, analog and/or digital electronic circuitry to process the imbalance input signals, and actuators to reposition the balance masses as required to implement the control effect. Improved automatic balancing systems are desired. One such system was disclosed and claimed in my prior U.S. patent application Ser. No. 08/635,076, filed on Apr. 19, 1996 and entitled "Pneumatically Driven Auto-balance Rotor Hub", now U.S. Pat. No. 5,860,865 issued on Jan. 19, 1999, which is incorporated herein in its entirety by reference. Provision of other auto-balance rotor hub arrangements are still desirable to provide automatic balancing of various types of rotated equipment, such as a turbine, propeller, yarn bobbin, flywheel, helicopter blades and the like.